A THEORY OF PURSUIT AND EVASION

Abstract : The purpose of this paper was to present an approach to the theory of pursuit and evasion with perfect information based only on general topological and set theoretical notions. The author's definition of the strategy is rather strange because multivalued strategies are allowed, such a strategy prescribes to a given motion of the enemy a whole class of possible motions. The schema adopted in this paper is general enough to enclose the pursuit and evasion with some restrictions on velocities or accelera tions (which may depend on the positions and directions of motions--for this reason any metric distance functions are introduced. The payoff function is the amount of time used by the pursuer and the evader to reach a configuration from a given set of final configurations.